We make that trip four times a year. I80 is the short route to/from Northern California but since you're already at I10, there's little difference in mileage between the routes. We usually make one on I80 and three on I10 because I've been staying with friends in NM's boot heel area.
I'd recommend you check maps for attractions you'd like to visit and choose a route that lets you see the ones of greatest interest to you. If you go through Tucson, try to make plans to stay there a day and visit the mirror lab at the university. It's the location where all of the mirrors for the next generation of giant telescopes are being made. If you're a member of a local museum, you may also have reciprocal visiting privileges and can get the tour for free.